روندیابی سیلاب با استفاده از مدل ماسکینگام با مشتق مرتبه کسری

نوع مقاله: مقاله پژوهشی

نویسندگان

1 کاندیدای دکتری سازه‌های آبی، گروه مهندسی آبیاری و آبادانی، دانشکده مهندسی و فناوری کشاورزی، دانشگاه تهران، کرج، ایران.

2 دانشیار، گروه مهندسی آبیاری و آبادانی دانشکده مهندسی و فناوری کشاورزی، دانشگاه تهران، کرج، ایران.

3 استادیار، گروه مهندسی آبیاری و آبادانی، دانشکده مهندسی و فناوری کشاورزی، دانشگاه تهران، کرج، ایران.

چکیده

مدل­های ماسکینگام موجود تنها در معادله ذخیره با یکدیگر متفاوت هستند. تاکنون به منظور لحاظ نمودن ویژگی غیرخطی موج سیلاب، ساختار معادله ذخیره بر اساس تجربه و به شیوه آزمون و خطا اصلاح شده است تا مشخصات کلی سیل دقیق­تر مدل شود. یکی از روش­های با مبنای تئوری برای لحاظ نمودن ویژگی­های غیرخطی در مدل روندیابی ماسکینگام، استفاده از مشتق مرتبه کسری در معادله دیفرانسیل پیوستگی است. تحقیق حاضر به ارائه مدل جدیدی از ماسکینگام می­پردازد که در آن از معادله خطی ذخیره و معادله دیفرانسیل پیوستگی از مرتبه کسری استفاده شده است. همان‌طور که در این تحقیق نشان داده شده است، مدل جدید قادر است هم سیلاب­های با رفتار خطی و هم رفتار غیرخطی را شبیه­سازی کند. مدل پیشنهادی ماسکینگام از مرتبه کسری، برای سه مجموعه­ی مختلف از داده­های سیل اجرا و آزمایش شد. نتایج این مطالعه نشان می­دهد که مدل ماسکینگام پیشنهادی منجر به بهبود نتایج می­شود و به طور مؤثر، ویژگی­های موج سیلاب را نسبت به مدل‌های سنتی ماسکینگام بهتر تخمین می­زند.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Flood Routing using Muskingum Model with Fractional Derivative

نویسندگان [English]

  • MirMohammad Bayrami 1
  • Alireza Vatankhah 2
  • Arezoo Nazi Ghameshlou 3
1 PhD Candidate of Water Structures, Department of Irrigation and Reclamation Engineering, Faculty of Agricultural Engineering and Technology, University College of Agriculture and Natural Resources, University of Tehran, Iran.
2 Associate Professor, Department of Irrigation and Reclamation Engineering, University College of Agriculture and Natural Resources, University of Tehran, P. O. Box 4111, Karaj, 31587-77871, Iran
3 Assistant Professor, Department of Irrigation and Reclamation Engineering, Faculty of Agricultural Engineering and Technology, University College of Agriculture and Natural Resources, University of Tehran, P. O. Box 4111, Karaj, 31587-77871, Iran.
چکیده [English]

The existing Muskingum models vary only in the form of the storage equation. So far, for accounting the nonlinearity characteristic of flood wave, the form of the storage equation has been modified based on the experience and in a trial and error manner in order to capture the overall flood propagating characteristics more accurately. One of the theoretical based method for considering the nonlinear characteristics in Muskingum model is to use the fractional derivative in the continuity differential equation. This study presents a new Muskingum model in which the linear storage equation and the continuity equation with fractional derivative are used. As shown in this study, the new model can simulate flood waves with both linear and nonlinear behaviors. The proposed Muskingum model with fractional derivative order was implemented and tested on three different sets of flood data. The results of this study indicate that the proposed Muskingum model improves the results and estimates the flood wave characteristics more accurately than the traditional linear Muskingum models.

کلیدواژه‌ها [English]

  • Flood routing
  • Nonlinear model
  • Hydrograph
  • Muskingum model
  • Fractional derivative

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